A study of ordered bi-Gamma-hyperideals in ordered Gamma-semihypergroups

Abstract

The main purpose of this paper is to investigate ordered

􀀀-semihypergroups in the general terms of ordered 􀀀-hyperideals. We intro-duce ordered (generalized) (m; n)-􀀀-hyperideals in ordered 􀀀-semihypergroups.

Then, we characterize ordered 􀀀-semihypergroup by ordered (generalized) (0; 2)-

􀀀-hyperideals, ordered (generalized) (1; 2)-􀀀{hyperideals and ordered (general-

ized) 0-minimal (0; 2)-􀀀-hyperideals. Furthermore, we investigate the notion of

ordered (generalized) (0; 2)-bi-􀀀-hyperideals, ordered 0-(0; 2) bisimple ordered

􀀀-semihypergroups and ordered 0-minimal (generalized) (0; 2)-bi-􀀀-hyperideals

in ordered 􀀀-semihyperoups. It is proved that an ordered 􀀀-semihypergroup

S with a zero 0 is 0-(0; 2)-bisimple if and only if it is left 0-simple.

Keywords

• algebraic hyperstructure,􀀀-subsemihypergroup,bisimple,or- dered 􀀀-semihypergroup

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